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Topics in Microeconometrics

Topics in Microeconometrics. William Greene Department of Economics Stern School of Business. Descriptive Statistics and Linear Regression. Model Building in Econometrics. Parameterizing the model Nonparametric analysis Semiparametric analysis Parametric analysis

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Topics in Microeconometrics

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  1. Topics in Microeconometrics William Greene Department of Economics Stern School of Business

  2. Descriptive Statistics and Linear Regression

  3. Model Building in Econometrics • Parameterizing the model • Nonparametric analysis • Semiparametric analysis • Parametric analysis • Sharpness of inferences follows from the strength of the assumptions A Model Relating (Log)Wage to Gender and Experience

  4. Semiparametric Regression: Least absolute deviations regression of y on x Application: Is there a relationship between investment and capital stock? Nonparametric Regression Kernel regression of y on x Parametric Regression: Least squares – maximum likelihood – regression of y on x

  5. Cornwell and Rupert Panel Data Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 YearsVariables in the file are EXP = work experienceWKS = weeks workedOCC = occupation, 1 if blue collar, IND = 1 if manufacturing industrySOUTH = 1 if resides in southSMSA = 1 if resides in a city (SMSA)MS = 1 if marriedFEM = 1 if femaleUNION = 1 if wage set by union contractED = years of educationBLK = 1 if individual is blackLWAGE = log of wage = dependent variable in regressions These data were analyzed in Cornwell, C. and Rupert, P., "Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators," Journal of Applied Econometrics, 3, 1988, pp. 149-155.  See Baltagi, page 122 for further analysis.  The data were downloaded from the website for Baltagi's text.

  6. A First Look at the DataDescriptive Statistics • Basic Measures of Location and Dispersion • Graphical Devices • Histogram • Kernel Density Estimator

  7. Histogram for LWAGE

  8. The kernel density estimator is ahistogram (of sorts).

  9. Kernel Estimator for LWAGE

  10. Kernel Density Estimator

  11. Objective: Impact of Education on (log) wage • Specification: What is the right model to use to analyze this association? • Estimation • Inference • Analysis

  12. Simple Linear Regression LWAGE = 5.8388 + 0.0652*ED

  13. Multiple Regression

  14. Specification: Quadratic Effect of Experience

  15. Partial Effects Education: .05544 Experience: .04062 – 2*.00068*Exp FEM – .37522

  16. Model Implication: Effect of Experience and Male vs. Female

  17. Hypothesis Test About Coefficients • Hypothesis • Null: Restriction on β: Rβ – q = 0 • Alternative: Not the null • Approaches • Fitting Criterion: R2 decrease under the null? • Wald: Rb – q close to 0 under the alternative?

  18. Hypotheses All Coefficients = 0? R = [ 0 | I ] q = [0] ED Coefficient = 0? R = 0,1,0,0,0,0,0,0,0,0,0,0 q = 0 No Experience effect? R = 0,0,1,0,0,0,0,0,0,0,0,0 0,0,0,1,0,0,0,0,0,0,0,0 q = 00

  19. Hypothesis Test Statistics

  20. Hypothesis: All Coefficients Equal Zero All Coefficients = 0? R = [0 | I] q = [0] R12 = .42645R02 = .00000 F = 280.7 with [11,4153] Wald = b2-12[V2-12]-1b2-12= 3087.83355 Note that Wald = JF = 11(280.7)

  21. Hypothesis: Education Effect = 0 ED Coefficient = 0? R = 0,1,0,0,0,0,0,0,0,0,0,0 q = 0 R12 = .42645R02 = .36355 (not shown) F = 455.396 Wald = (.05544-0)2/(.0026)2= 455.396 Note F = t2 and Wald = F For a single hypothesis about 1 coefficient.

  22. Hypothesis: Experience Effect = 0 No Experience effect? R = 0,0,1,0,0,0,0,0,0,0,0,0 0,0,0,1,0,0,0,0,0,0,0,0 q = 00R02 = .34101, R12 = .42645F = 309.33 Wald = 618.601 (W* = 5.99)

  23. A Robust Covariance Matrix • What does robustness mean? • Robust to: • Heteroscedasticty • Not robust to: • Autocorrelation • Individual heterogeneity • The wrong model specification • ‘Robust inference’

  24. Robust Covariance Matrix Heteroscedasticity Robust Covariance Matrix

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